Question: Solve for $x$ and $y$ using elimination. ${-3x-3y = -27}$ ${-2x+3y = -3}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3y$ and $3y$ cancel out. $-5x = -30$ $\dfrac{-5x}{{-5}} = \dfrac{-30}{{-5}}$ ${x = 6}$ Now that you know ${x = 6}$ , plug it back into $\thinspace {-3x-3y = -27}\thinspace$ to find $y$ ${-3}{(6)}{ - 3y = -27}$ $-18-3y = -27$ $-18{+18} - 3y = -27{+18}$ $-3y = -9$ $\dfrac{-3y}{{-3}} = \dfrac{-9}{{-3}}$ ${y = 3}$ You can also plug ${x = 6}$ into $\thinspace {-2x+3y = -3}\thinspace$ and get the same answer for $y$ : ${-2}{(6)}{ + 3y = -3}$ ${y = 3}$